Properties

Label 225.2.q.a.121.22
Level $225$
Weight $2$
Character 225.121
Analytic conductor $1.797$
Analytic rank $0$
Dimension $224$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(16,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.q (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 121.22
Character \(\chi\) \(=\) 225.121
Dual form 225.2.q.a.106.22

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.62705 - 0.345839i) q^{2} +(1.73185 + 0.0263451i) q^{3} +(0.700584 - 0.311920i) q^{4} +(-0.380412 - 2.20347i) q^{5} +(2.82691 - 0.556077i) q^{6} +(0.694163 + 1.20233i) q^{7} +(-1.65942 + 1.20564i) q^{8} +(2.99861 + 0.0912516i) q^{9} +(-1.38100 - 3.45359i) q^{10} +(-4.44787 + 0.945423i) q^{11} +(1.22152 - 0.521742i) q^{12} +(-0.664131 - 0.141165i) q^{13} +(1.54525 + 1.71617i) q^{14} +(-0.600766 - 3.82611i) q^{15} +(-3.30929 + 3.67534i) q^{16} +(-1.73545 + 1.26088i) q^{17} +(4.91044 - 0.888568i) q^{18} +(5.56870 - 4.04590i) q^{19} +(-0.953818 - 1.42506i) q^{20} +(1.17051 + 2.10054i) q^{21} +(-6.90992 + 3.07649i) q^{22} +(-0.0716950 - 0.0796254i) q^{23} +(-2.90563 + 2.04427i) q^{24} +(-4.71057 + 1.67645i) q^{25} -1.12939 q^{26} +(5.19074 + 0.237033i) q^{27} +(0.861350 + 0.625807i) q^{28} +(-0.214650 + 2.04226i) q^{29} +(-2.30069 - 6.01748i) q^{30} +(0.675922 + 6.43096i) q^{31} +(-2.06213 + 3.57172i) q^{32} +(-7.72795 + 1.52015i) q^{33} +(-2.38760 + 2.65170i) q^{34} +(2.38522 - 1.98695i) q^{35} +(2.12924 - 0.871398i) q^{36} +(-0.886060 - 2.72701i) q^{37} +(7.66130 - 8.50874i) q^{38} +(-1.14646 - 0.261974i) q^{39} +(3.28786 + 3.19785i) q^{40} +(-5.31403 - 1.12953i) q^{41} +(2.63092 + 3.01286i) q^{42} +(-0.613014 - 1.06177i) q^{43} +(-2.82121 + 2.04973i) q^{44} +(-0.939638 - 6.64207i) q^{45} +(-0.144189 - 0.104759i) q^{46} +(1.23665 - 11.7660i) q^{47} +(-5.82802 + 6.27796i) q^{48} +(2.53627 - 4.39296i) q^{49} +(-7.08454 + 4.35677i) q^{50} +(-3.03876 + 2.13793i) q^{51} +(-0.509312 + 0.108258i) q^{52} +(-1.07586 - 0.781661i) q^{53} +(8.52756 - 1.40950i) q^{54} +(3.77524 + 9.44110i) q^{55} +(-2.60148 - 1.15825i) q^{56} +(9.75074 - 6.86018i) q^{57} +(0.357048 + 3.39709i) q^{58} +(1.69407 + 0.360086i) q^{59} +(-1.61433 - 2.49312i) q^{60} +(3.69259 - 0.784884i) q^{61} +(3.32384 + 10.2297i) q^{62} +(1.97181 + 3.66865i) q^{63} +(0.936638 - 2.88268i) q^{64} +(-0.0584104 + 1.51709i) q^{65} +(-12.0480 + 5.14599i) q^{66} +(1.48608 + 14.1391i) q^{67} +(-0.822536 + 1.42467i) q^{68} +(-0.122067 - 0.139788i) q^{69} +(3.19370 - 4.05776i) q^{70} +(-10.9600 - 7.96294i) q^{71} +(-5.08598 + 3.46382i) q^{72} +(-1.83085 + 5.63478i) q^{73} +(-2.38477 - 4.13054i) q^{74} +(-8.20217 + 2.77927i) q^{75} +(2.63935 - 4.57148i) q^{76} +(-4.22425 - 4.69151i) q^{77} +(-1.95594 - 0.0297540i) q^{78} +(0.938478 - 8.92902i) q^{79} +(9.35740 + 5.89378i) q^{80} +(8.98335 + 0.547256i) q^{81} -9.03682 q^{82} +(16.5673 + 7.37623i) q^{83} +(1.47524 + 1.10650i) q^{84} +(3.43850 + 3.34436i) q^{85} +(-1.36460 - 1.51555i) q^{86} +(-0.425545 + 3.53123i) q^{87} +(6.24105 - 6.93138i) q^{88} +(2.33361 - 7.18212i) q^{89} +(-3.82592 - 10.4820i) q^{90} +(-0.291288 - 0.896494i) q^{91} +(-0.0750652 - 0.0334212i) q^{92} +(1.00117 + 11.1553i) q^{93} +(-2.05704 - 19.5715i) q^{94} +(-11.0334 - 10.7314i) q^{95} +(-3.66541 + 6.13136i) q^{96} +(-1.13640 + 10.8121i) q^{97} +(2.60738 - 8.02469i) q^{98} +(-13.4237 + 2.42908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.62705 0.345839i 1.15050 0.244545i 0.407091 0.913388i \(-0.366543\pi\)
0.743404 + 0.668842i \(0.233210\pi\)
\(3\) 1.73185 + 0.0263451i 0.999884 + 0.0152104i
\(4\) 0.700584 0.311920i 0.350292 0.155960i
\(5\) −0.380412 2.20347i −0.170126 0.985422i
\(6\) 2.82691 0.556077i 1.15408 0.227018i
\(7\) 0.694163 + 1.20233i 0.262369 + 0.454436i 0.966871 0.255266i \(-0.0821629\pi\)
−0.704502 + 0.709702i \(0.748830\pi\)
\(8\) −1.65942 + 1.20564i −0.586694 + 0.426258i
\(9\) 2.99861 + 0.0912516i 0.999537 + 0.0304172i
\(10\) −1.38100 3.45359i −0.436709 1.09212i
\(11\) −4.44787 + 0.945423i −1.34108 + 0.285056i −0.821912 0.569615i \(-0.807092\pi\)
−0.519170 + 0.854671i \(0.673759\pi\)
\(12\) 1.22152 0.521742i 0.352624 0.150614i
\(13\) −0.664131 0.141165i −0.184197 0.0391522i 0.114890 0.993378i \(-0.463349\pi\)
−0.299086 + 0.954226i \(0.596682\pi\)
\(14\) 1.54525 + 1.71617i 0.412985 + 0.458666i
\(15\) −0.600766 3.82611i −0.155117 0.987896i
\(16\) −3.30929 + 3.67534i −0.827323 + 0.918835i
\(17\) −1.73545 + 1.26088i −0.420909 + 0.305808i −0.778003 0.628260i \(-0.783767\pi\)
0.357095 + 0.934068i \(0.383767\pi\)
\(18\) 4.91044 0.888568i 1.15740 0.209437i
\(19\) 5.56870 4.04590i 1.27755 0.928192i 0.278071 0.960560i \(-0.410305\pi\)
0.999476 + 0.0323680i \(0.0103049\pi\)
\(20\) −0.953818 1.42506i −0.213280 0.318653i
\(21\) 1.17051 + 2.10054i 0.255427 + 0.458375i
\(22\) −6.90992 + 3.07649i −1.47320 + 0.655911i
\(23\) −0.0716950 0.0796254i −0.0149494 0.0166030i 0.735624 0.677390i \(-0.236889\pi\)
−0.750573 + 0.660787i \(0.770223\pi\)
\(24\) −2.90563 + 2.04427i −0.593110 + 0.417285i
\(25\) −4.71057 + 1.67645i −0.942115 + 0.335291i
\(26\) −1.12939 −0.221492
\(27\) 5.19074 + 0.237033i 0.998959 + 0.0456170i
\(28\) 0.861350 + 0.625807i 0.162780 + 0.118266i
\(29\) −0.214650 + 2.04226i −0.0398595 + 0.379238i 0.956348 + 0.292230i \(0.0943973\pi\)
−0.996208 + 0.0870081i \(0.972269\pi\)
\(30\) −2.30069 6.01748i −0.420047 1.09864i
\(31\) 0.675922 + 6.43096i 0.121399 + 1.15504i 0.870358 + 0.492419i \(0.163887\pi\)
−0.748959 + 0.662616i \(0.769446\pi\)
\(32\) −2.06213 + 3.57172i −0.364537 + 0.631397i
\(33\) −7.72795 + 1.52015i −1.34526 + 0.264625i
\(34\) −2.38760 + 2.65170i −0.409470 + 0.454762i
\(35\) 2.38522 1.98695i 0.403176 0.335856i
\(36\) 2.12924 0.871398i 0.354874 0.145233i
\(37\) −0.886060 2.72701i −0.145667 0.448318i 0.851429 0.524470i \(-0.175737\pi\)
−0.997096 + 0.0761520i \(0.975737\pi\)
\(38\) 7.66130 8.50874i 1.24283 1.38030i
\(39\) −1.14646 0.261974i −0.183580 0.0419494i
\(40\) 3.28786 + 3.19785i 0.519856 + 0.505624i
\(41\) −5.31403 1.12953i −0.829913 0.176403i −0.226681 0.973969i \(-0.572787\pi\)
−0.603232 + 0.797566i \(0.706121\pi\)
\(42\) 2.63092 + 3.01286i 0.405960 + 0.464895i
\(43\) −0.613014 1.06177i −0.0934837 0.161919i 0.815491 0.578770i \(-0.196467\pi\)
−0.908975 + 0.416851i \(0.863134\pi\)
\(44\) −2.82121 + 2.04973i −0.425313 + 0.309008i
\(45\) −0.939638 6.64207i −0.140073 0.990141i
\(46\) −0.144189 0.104759i −0.0212595 0.0154459i
\(47\) 1.23665 11.7660i 0.180385 1.71624i −0.412501 0.910957i \(-0.635345\pi\)
0.592885 0.805287i \(-0.297989\pi\)
\(48\) −5.82802 + 6.27796i −0.841203 + 0.906145i
\(49\) 2.53627 4.39296i 0.362325 0.627565i
\(50\) −7.08454 + 4.35677i −1.00190 + 0.616141i
\(51\) −3.03876 + 2.13793i −0.425512 + 0.299371i
\(52\) −0.509312 + 0.108258i −0.0706289 + 0.0150126i
\(53\) −1.07586 0.781661i −0.147781 0.107369i 0.511438 0.859320i \(-0.329113\pi\)
−0.659219 + 0.751951i \(0.729113\pi\)
\(54\) 8.52756 1.40950i 1.16045 0.191809i
\(55\) 3.77524 + 9.44110i 0.509053 + 1.27304i
\(56\) −2.60148 1.15825i −0.347638 0.154778i
\(57\) 9.75074 6.86018i 1.29152 0.908653i
\(58\) 0.357048 + 3.39709i 0.0468827 + 0.446059i
\(59\) 1.69407 + 0.360086i 0.220549 + 0.0468792i 0.316861 0.948472i \(-0.397371\pi\)
−0.0963115 + 0.995351i \(0.530705\pi\)
\(60\) −1.61433 2.49312i −0.208409 0.321860i
\(61\) 3.69259 0.784884i 0.472788 0.100494i 0.0346452 0.999400i \(-0.488970\pi\)
0.438142 + 0.898906i \(0.355637\pi\)
\(62\) 3.32384 + 10.2297i 0.422128 + 1.29918i
\(63\) 1.97181 + 3.66865i 0.248425 + 0.462207i
\(64\) 0.936638 2.88268i 0.117080 0.360334i
\(65\) −0.0584104 + 1.51709i −0.00724492 + 0.188172i
\(66\) −12.0480 + 5.14599i −1.48301 + 0.633427i
\(67\) 1.48608 + 14.1391i 0.181553 + 1.72737i 0.583854 + 0.811858i \(0.301544\pi\)
−0.402301 + 0.915508i \(0.631789\pi\)
\(68\) −0.822536 + 1.42467i −0.0997472 + 0.172767i
\(69\) −0.122067 0.139788i −0.0146952 0.0168285i
\(70\) 3.19370 4.05776i 0.381721 0.484995i
\(71\) −10.9600 7.96294i −1.30072 0.945027i −0.300755 0.953701i \(-0.597239\pi\)
−0.999962 + 0.00867479i \(0.997239\pi\)
\(72\) −5.08598 + 3.46382i −0.599388 + 0.408215i
\(73\) −1.83085 + 5.63478i −0.214285 + 0.659501i 0.784919 + 0.619599i \(0.212705\pi\)
−0.999204 + 0.0399023i \(0.987295\pi\)
\(74\) −2.38477 4.13054i −0.277224 0.480166i
\(75\) −8.20217 + 2.77927i −0.947106 + 0.320922i
\(76\) 2.63935 4.57148i 0.302754 0.524385i
\(77\) −4.22425 4.69151i −0.481398 0.534647i
\(78\) −1.95594 0.0297540i −0.221466 0.00336897i
\(79\) 0.938478 8.92902i 0.105587 1.00459i −0.805561 0.592513i \(-0.798136\pi\)
0.911148 0.412080i \(-0.135198\pi\)
\(80\) 9.35740 + 5.89378i 1.04619 + 0.658945i
\(81\) 8.98335 + 0.547256i 0.998150 + 0.0608062i
\(82\) −9.03682 −0.997950
\(83\) 16.5673 + 7.37623i 1.81850 + 0.809647i 0.948653 + 0.316320i \(0.102447\pi\)
0.869844 + 0.493327i \(0.164219\pi\)
\(84\) 1.47524 + 1.10650i 0.160962 + 0.120729i
\(85\) 3.43850 + 3.34436i 0.372958 + 0.362747i
\(86\) −1.36460 1.51555i −0.147149 0.163426i
\(87\) −0.425545 + 3.53123i −0.0456233 + 0.378588i
\(88\) 6.24105 6.93138i 0.665298 0.738888i
\(89\) 2.33361 7.18212i 0.247363 0.761304i −0.747876 0.663838i \(-0.768926\pi\)
0.995239 0.0974656i \(-0.0310736\pi\)
\(90\) −3.82592 10.4820i −0.403288 1.10490i
\(91\) −0.291288 0.896494i −0.0305353 0.0939781i
\(92\) −0.0750652 0.0334212i −0.00782608 0.00348440i
\(93\) 1.00117 + 11.1553i 0.103817 + 1.15675i
\(94\) −2.05704 19.5715i −0.212168 2.01864i
\(95\) −11.0334 10.7314i −1.13200 1.10101i
\(96\) −3.66541 + 6.13136i −0.374099 + 0.625779i
\(97\) −1.13640 + 10.8121i −0.115384 + 1.09781i 0.771633 + 0.636068i \(0.219440\pi\)
−0.887017 + 0.461737i \(0.847226\pi\)
\(98\) 2.60738 8.02469i 0.263385 0.810616i
\(99\) −13.4237 + 2.42908i −1.34913 + 0.244132i
\(100\) −2.77723 + 2.64382i −0.277723 + 0.264382i
\(101\) −6.10657 10.5769i −0.607626 1.05244i −0.991630 0.129108i \(-0.958788\pi\)
0.384004 0.923331i \(-0.374545\pi\)
\(102\) −4.20482 + 4.52944i −0.416340 + 0.448481i
\(103\) −0.775688 + 0.345359i −0.0764309 + 0.0340292i −0.444596 0.895731i \(-0.646653\pi\)
0.368165 + 0.929760i \(0.379986\pi\)
\(104\) 1.27227 0.566450i 0.124756 0.0555450i
\(105\) 4.18320 3.37826i 0.408238 0.329684i
\(106\) −2.02081 0.899723i −0.196278 0.0873888i
\(107\) 19.0764 1.84419 0.922095 0.386964i \(-0.126476\pi\)
0.922095 + 0.386964i \(0.126476\pi\)
\(108\) 3.71049 1.45304i 0.357042 0.139818i
\(109\) 4.05014 + 12.4651i 0.387933 + 1.19394i 0.934330 + 0.356409i \(0.115999\pi\)
−0.546397 + 0.837526i \(0.684001\pi\)
\(110\) 9.40759 + 14.0555i 0.896978 + 1.34014i
\(111\) −1.46268 4.74612i −0.138831 0.450482i
\(112\) −6.71614 1.42756i −0.634616 0.134892i
\(113\) 6.81089 + 1.44770i 0.640714 + 0.136188i 0.516802 0.856105i \(-0.327122\pi\)
0.123913 + 0.992293i \(0.460456\pi\)
\(114\) 13.4924 14.5340i 1.26368 1.36124i
\(115\) −0.148179 + 0.188268i −0.0138177 + 0.0175561i
\(116\) 0.486642 + 1.49773i 0.0451835 + 0.139061i
\(117\) −1.97859 0.483903i −0.182921 0.0447369i
\(118\) 2.88087 0.265205
\(119\) −2.72067 1.21132i −0.249404 0.111042i
\(120\) 5.60983 + 5.62481i 0.512105 + 0.513473i
\(121\) 8.84069 3.93613i 0.803699 0.357830i
\(122\) 5.73657 2.55409i 0.519365 0.231236i
\(123\) −9.17336 2.09618i −0.827134 0.189006i
\(124\) 2.47949 + 4.29460i 0.222665 + 0.385666i
\(125\) 5.48598 + 9.74187i 0.490681 + 0.871339i
\(126\) 4.47699 + 5.28714i 0.398842 + 0.471016i
\(127\) 6.85641 21.1019i 0.608408 1.87249i 0.137000 0.990571i \(-0.456254\pi\)
0.471407 0.881916i \(-0.343746\pi\)
\(128\) 1.38922 13.2175i 0.122791 1.16828i
\(129\) −1.03368 1.85498i −0.0910101 0.163322i
\(130\) 0.429635 + 2.48858i 0.0376814 + 0.218263i
\(131\) 1.21480 + 11.5581i 0.106138 + 1.00983i 0.909885 + 0.414862i \(0.136170\pi\)
−0.803747 + 0.594972i \(0.797163\pi\)
\(132\) −4.93991 + 3.47550i −0.429964 + 0.302503i
\(133\) 8.73007 + 3.88688i 0.756993 + 0.337035i
\(134\) 7.30778 + 22.4910i 0.631296 + 1.94293i
\(135\) −1.45233 11.5278i −0.124996 0.992157i
\(136\) 1.35968 4.18466i 0.116591 0.358832i
\(137\) −11.0828 + 12.3087i −0.946869 + 1.05160i 0.0517289 + 0.998661i \(0.483527\pi\)
−0.998598 + 0.0529430i \(0.983140\pi\)
\(138\) −0.246953 0.185226i −0.0210221 0.0157675i
\(139\) −11.2616 12.5073i −0.955198 1.06085i −0.998090 0.0617748i \(-0.980324\pi\)
0.0428925 0.999080i \(-0.486343\pi\)
\(140\) 1.05128 2.13602i 0.0888494 0.180527i
\(141\) 2.45168 20.3443i 0.206468 1.71330i
\(142\) −20.5864 9.16565i −1.72757 0.769164i
\(143\) 3.08743 0.258184
\(144\) −10.2587 + 10.7189i −0.854888 + 0.893245i
\(145\) 4.58172 0.303925i 0.380491 0.0252396i
\(146\) −1.03015 + 9.80123i −0.0852559 + 0.811155i
\(147\) 4.50818 7.54113i 0.371829 0.621982i
\(148\) −1.47137 1.63412i −0.120946 0.134324i
\(149\) −7.97992 + 13.8216i −0.653740 + 1.13231i 0.328468 + 0.944515i \(0.393468\pi\)
−0.982208 + 0.187796i \(0.939865\pi\)
\(150\) −12.3841 + 7.35863i −1.01116 + 0.600830i
\(151\) −4.20769 7.28793i −0.342417 0.593084i 0.642464 0.766316i \(-0.277912\pi\)
−0.984881 + 0.173232i \(0.944579\pi\)
\(152\) −4.36292 + 13.4277i −0.353880 + 1.08913i
\(153\) −5.31900 + 3.62253i −0.430016 + 0.292864i
\(154\) −8.49556 6.17239i −0.684592 0.497385i
\(155\) 13.9133 3.93579i 1.11754 0.316130i
\(156\) −0.884904 + 0.174068i −0.0708490 + 0.0139366i
\(157\) 0.0425739 0.0737402i 0.00339777 0.00588511i −0.864322 0.502940i \(-0.832252\pi\)
0.867719 + 0.497055i \(0.165585\pi\)
\(158\) −1.56106 14.8525i −0.124191 1.18160i
\(159\) −1.84264 1.38206i −0.146131 0.109605i
\(160\) 8.65465 + 3.18513i 0.684210 + 0.251806i
\(161\) 0.0459676 0.141474i 0.00362275 0.0111497i
\(162\) 14.8056 2.21638i 1.16324 0.174136i
\(163\) 3.81218 + 11.7327i 0.298593 + 0.918974i 0.981991 + 0.188928i \(0.0605013\pi\)
−0.683398 + 0.730046i \(0.739499\pi\)
\(164\) −4.07525 + 0.866222i −0.318224 + 0.0676406i
\(165\) 6.28942 + 16.4500i 0.489630 + 1.28063i
\(166\) 29.5067 + 6.27185i 2.29017 + 0.486790i
\(167\) 0.700044 + 6.66047i 0.0541710 + 0.515403i 0.987639 + 0.156743i \(0.0500994\pi\)
−0.933468 + 0.358660i \(0.883234\pi\)
\(168\) −4.47486 2.07446i −0.345243 0.160048i
\(169\) −11.4549 5.10007i −0.881150 0.392313i
\(170\) 6.75121 + 4.25227i 0.517794 + 0.326134i
\(171\) 17.0676 11.6239i 1.30519 0.888904i
\(172\) −0.760656 0.552649i −0.0579995 0.0421391i
\(173\) −11.2482 + 2.39087i −0.855181 + 0.181774i −0.614585 0.788851i \(-0.710676\pi\)
−0.240596 + 0.970625i \(0.577343\pi\)
\(174\) 0.528857 + 5.89265i 0.0400926 + 0.446721i
\(175\) −5.28555 4.49991i −0.399550 0.340161i
\(176\) 11.2445 19.4761i 0.847588 1.46807i
\(177\) 2.92439 + 0.668246i 0.219811 + 0.0502284i
\(178\) 1.31304 12.4927i 0.0984162 0.936368i
\(179\) −3.97320 2.88670i −0.296971 0.215762i 0.429315 0.903155i \(-0.358755\pi\)
−0.726286 + 0.687393i \(0.758755\pi\)
\(180\) −2.73009 4.36024i −0.203489 0.324993i
\(181\) −1.69167 + 1.22907i −0.125741 + 0.0913562i −0.648878 0.760892i \(-0.724762\pi\)
0.523137 + 0.852248i \(0.324762\pi\)
\(182\) −0.783983 1.35790i −0.0581127 0.100654i
\(183\) 6.41569 1.26202i 0.474261 0.0932912i
\(184\) 0.214972 + 0.0456937i 0.0158479 + 0.00336858i
\(185\) −5.67183 + 2.98980i −0.417001 + 0.219814i
\(186\) 5.48688 + 17.8039i 0.402318 + 1.30545i
\(187\) 6.52699 7.24896i 0.477301 0.530096i
\(188\) −2.80367 8.62880i −0.204478 0.629320i
\(189\) 3.31823 + 6.40550i 0.241366 + 0.465932i
\(190\) −21.6632 13.6446i −1.57161 0.989886i
\(191\) 6.87172 7.63182i 0.497220 0.552219i −0.441337 0.897341i \(-0.645496\pi\)
0.938558 + 0.345122i \(0.112162\pi\)
\(192\) 1.69806 4.96769i 0.122547 0.358512i
\(193\) 0.879316 1.52302i 0.0632945 0.109629i −0.832642 0.553812i \(-0.813173\pi\)
0.895936 + 0.444183i \(0.146506\pi\)
\(194\) 1.89028 + 17.9848i 0.135714 + 1.29124i
\(195\) −0.141126 + 2.62584i −0.0101062 + 0.188040i
\(196\) 0.406622 3.86875i 0.0290444 0.276339i
\(197\) 1.28192 + 0.931373i 0.0913333 + 0.0663576i 0.632515 0.774548i \(-0.282023\pi\)
−0.541181 + 0.840906i \(0.682023\pi\)
\(198\) −21.0009 + 8.59467i −1.49247 + 0.610797i
\(199\) −4.83781 −0.342943 −0.171471 0.985189i \(-0.554852\pi\)
−0.171471 + 0.985189i \(0.554852\pi\)
\(200\) 5.79563 8.46120i 0.409813 0.598297i
\(201\) 2.20117 + 24.5260i 0.155259 + 1.72993i
\(202\) −13.5936 15.0972i −0.956441 1.06224i
\(203\) −2.60446 + 1.15958i −0.182798 + 0.0813867i
\(204\) −1.46204 + 2.44565i −0.102364 + 0.171230i
\(205\) −0.467370 + 12.1390i −0.0326425 + 0.847825i
\(206\) −1.14264 + 0.830178i −0.0796117 + 0.0578413i
\(207\) −0.207720 0.245308i −0.0144375 0.0170501i
\(208\) 2.71663 1.97375i 0.188365 0.136855i
\(209\) −20.9437 + 23.2604i −1.44871 + 1.60895i
\(210\) 5.63792 6.94330i 0.389053 0.479133i
\(211\) −2.87300 3.19079i −0.197785 0.219663i 0.636091 0.771614i \(-0.280550\pi\)
−0.833877 + 0.551951i \(0.813884\pi\)
\(212\) −0.997550 0.212036i −0.0685120 0.0145627i
\(213\) −18.7714 14.0794i −1.28619 0.964702i
\(214\) 31.0383 6.59739i 2.12173 0.450988i
\(215\) −2.10638 + 1.75467i −0.143654 + 0.119667i
\(216\) −8.89941 + 5.86483i −0.605528 + 0.399051i
\(217\) −7.26291 + 5.27682i −0.493039 + 0.358214i
\(218\) 10.9007 + 18.8805i 0.738287 + 1.27875i
\(219\) −3.31921 + 9.71036i −0.224291 + 0.656165i
\(220\) 5.58974 + 5.43671i 0.376860 + 0.366543i
\(221\) 1.33056 0.592403i 0.0895031 0.0398494i
\(222\) −4.02125 7.21631i −0.269888 0.484327i
\(223\) −15.8538 + 3.36984i −1.06165 + 0.225661i −0.705459 0.708751i \(-0.749259\pi\)
−0.356193 + 0.934412i \(0.615926\pi\)
\(224\) −5.72583 −0.382573
\(225\) −14.2782 + 4.59719i −0.951877 + 0.306479i
\(226\) 11.5823 0.770443
\(227\) −9.01077 + 1.91530i −0.598066 + 0.127123i −0.496990 0.867756i \(-0.665562\pi\)
−0.101075 + 0.994879i \(0.532228\pi\)
\(228\) 4.69139 7.84759i 0.310695 0.519719i
\(229\) −7.49545 + 3.33719i −0.495314 + 0.220528i −0.639162 0.769072i \(-0.720719\pi\)
0.143849 + 0.989600i \(0.454052\pi\)
\(230\) −0.175983 + 0.357567i −0.0116040 + 0.0235773i
\(231\) −7.19217 8.23628i −0.473210 0.541907i
\(232\) −2.10604 3.64776i −0.138268 0.239487i
\(233\) −6.70215 + 4.86940i −0.439073 + 0.319005i −0.785266 0.619158i \(-0.787474\pi\)
0.346194 + 0.938163i \(0.387474\pi\)
\(234\) −3.38661 0.103059i −0.221390 0.00673717i
\(235\) −26.3964 + 1.75099i −1.72191 + 0.114222i
\(236\) 1.29916 0.276145i 0.0845680 0.0179755i
\(237\) 1.86054 15.4390i 0.120855 1.00287i
\(238\) −4.84559 1.02996i −0.314093 0.0667625i
\(239\) 0.722110 + 0.801984i 0.0467094 + 0.0518760i 0.766047 0.642785i \(-0.222221\pi\)
−0.719337 + 0.694661i \(0.755554\pi\)
\(240\) 16.0503 + 10.4537i 1.03605 + 0.674782i
\(241\) −16.7927 + 18.6502i −1.08172 + 1.20137i −0.103315 + 0.994649i \(0.532945\pi\)
−0.978401 + 0.206718i \(0.933722\pi\)
\(242\) 13.0229 9.46173i 0.837147 0.608223i
\(243\) 15.5434 + 1.18443i 0.997109 + 0.0759814i
\(244\) 2.34215 1.70167i 0.149941 0.108938i
\(245\) −10.6446 3.91748i −0.680058 0.250278i
\(246\) −15.6504 0.238076i −0.997834 0.0151792i
\(247\) −4.26949 + 1.90090i −0.271661 + 0.120951i
\(248\) −8.87507 9.85676i −0.563567 0.625905i
\(249\) 28.4977 + 13.2110i 1.80597 + 0.837213i
\(250\) 12.2951 + 13.9532i 0.777608 + 0.882478i
\(251\) −23.1900 −1.46374 −0.731869 0.681445i \(-0.761352\pi\)
−0.731869 + 0.681445i \(0.761352\pi\)
\(252\) 2.52575 + 1.95515i 0.159107 + 0.123163i
\(253\) 0.394169 + 0.286381i 0.0247812 + 0.0180046i
\(254\) 3.85784 36.7049i 0.242062 2.30307i
\(255\) 5.86686 + 5.88253i 0.367397 + 0.368378i
\(256\) −1.67716 15.9571i −0.104823 0.997321i
\(257\) −10.4244 + 18.0555i −0.650253 + 1.12627i 0.332808 + 0.942995i \(0.392004\pi\)
−0.983061 + 0.183277i \(0.941329\pi\)
\(258\) −2.32336 2.66065i −0.144646 0.165645i
\(259\) 2.66369 2.95833i 0.165514 0.183821i
\(260\) 0.432291 + 1.08107i 0.0268096 + 0.0670452i
\(261\) −0.830012 + 6.10436i −0.0513764 + 0.377850i
\(262\) 5.97377 + 18.3854i 0.369061 + 1.13585i
\(263\) −6.07004 + 6.74146i −0.374295 + 0.415696i −0.900634 0.434578i \(-0.856897\pi\)
0.526339 + 0.850275i \(0.323564\pi\)
\(264\) 10.9912 11.8397i 0.676460 0.728683i
\(265\) −1.31310 + 2.66799i −0.0806629 + 0.163893i
\(266\) 15.5485 + 3.30493i 0.953338 + 0.202638i
\(267\) 4.23068 12.3769i 0.258914 0.757453i
\(268\) 5.45140 + 9.44209i 0.332997 + 0.576768i
\(269\) 12.0005 8.71886i 0.731683 0.531599i −0.158413 0.987373i \(-0.550638\pi\)
0.890095 + 0.455774i \(0.150638\pi\)
\(270\) −6.34978 18.2540i −0.386435 1.11091i
\(271\) 6.34725 + 4.61155i 0.385568 + 0.280132i 0.763637 0.645646i \(-0.223412\pi\)
−0.378069 + 0.925777i \(0.623412\pi\)
\(272\) 1.10895 10.5510i 0.0672402 0.639748i
\(273\) −0.480850 1.56027i −0.0291024 0.0944316i
\(274\) −13.7754 + 23.8597i −0.832203 + 1.44142i
\(275\) 19.3670 11.9101i 1.16788 0.718208i
\(276\) −0.129121 0.0598580i −0.00777218 0.00360303i
\(277\) 21.7610 4.62545i 1.30749 0.277916i 0.499092 0.866549i \(-0.333667\pi\)
0.808400 + 0.588633i \(0.200334\pi\)
\(278\) −22.6487 16.4552i −1.35838 0.986919i
\(279\) 1.43999 + 19.3456i 0.0862100 + 1.15819i
\(280\) −1.56255 + 6.17291i −0.0933799 + 0.368902i
\(281\) 9.27859 + 4.13109i 0.553514 + 0.246440i 0.664380 0.747395i \(-0.268696\pi\)
−0.110866 + 0.993835i \(0.535362\pi\)
\(282\) −3.04688 33.9491i −0.181439 2.02164i
\(283\) −0.0797346 0.758624i −0.00473973 0.0450955i 0.991896 0.127049i \(-0.0405507\pi\)
−0.996636 + 0.0819538i \(0.973884\pi\)
\(284\) −10.1622 2.16005i −0.603018 0.128175i
\(285\) −18.8255 18.8758i −1.11513 1.11811i
\(286\) 5.02339 1.06775i 0.297039 0.0631376i
\(287\) −2.33074 7.17328i −0.137579 0.423425i
\(288\) −6.50947 + 10.5220i −0.383574 + 0.620017i
\(289\) −3.83131 + 11.7916i −0.225371 + 0.693622i
\(290\) 7.34956 2.07904i 0.431581 0.122085i
\(291\) −2.25292 + 18.6950i −0.132069 + 1.09592i
\(292\) 0.474936 + 4.51872i 0.0277935 + 0.264438i
\(293\) 3.29507 5.70722i 0.192500 0.333419i −0.753578 0.657358i \(-0.771674\pi\)
0.946078 + 0.323939i \(0.105007\pi\)
\(294\) 4.72700 13.8289i 0.275684 0.806516i
\(295\) 0.148994 3.86982i 0.00867476 0.225310i
\(296\) 4.75815 + 3.45699i 0.276562 + 0.200934i
\(297\) −23.3118 + 3.85316i −1.35269 + 0.223583i
\(298\) −8.20364 + 25.2482i −0.475224 + 1.46259i
\(299\) 0.0363745 + 0.0630025i 0.00210359 + 0.00364353i
\(300\) −4.87941 + 4.50554i −0.281713 + 0.260127i
\(301\) 0.851063 1.47408i 0.0490545 0.0849648i
\(302\) −9.36656 10.4026i −0.538985 0.598604i
\(303\) −10.2970 18.4785i −0.591548 1.06156i
\(304\) −3.55840 + 33.8559i −0.204088 + 1.94177i
\(305\) −3.13418 7.83794i −0.179462 0.448799i
\(306\) −7.40145 + 7.73354i −0.423113 + 0.442097i
\(307\) 20.2069 1.15327 0.576634 0.817002i \(-0.304366\pi\)
0.576634 + 0.817002i \(0.304366\pi\)
\(308\) −4.42282 1.96917i −0.252014 0.112204i
\(309\) −1.35247 + 0.577674i −0.0769396 + 0.0328627i
\(310\) 21.2765 11.2155i 1.20842 0.636997i
\(311\) 11.9608 + 13.2838i 0.678234 + 0.753255i 0.979754 0.200205i \(-0.0641608\pi\)
−0.301520 + 0.953460i \(0.597494\pi\)
\(312\) 2.21830 0.947489i 0.125587 0.0536410i
\(313\) 12.2784 13.6366i 0.694019 0.770786i −0.288393 0.957512i \(-0.593121\pi\)
0.982412 + 0.186726i \(0.0597877\pi\)
\(314\) 0.0437675 0.134702i 0.00246994 0.00760170i
\(315\) 7.33367 5.74043i 0.413205 0.323437i
\(316\) −2.12766 6.54826i −0.119690 0.368369i
\(317\) 2.89860 + 1.29054i 0.162802 + 0.0724841i 0.486520 0.873670i \(-0.338266\pi\)
−0.323718 + 0.946154i \(0.604933\pi\)
\(318\) −3.47604 1.61142i −0.194927 0.0903641i
\(319\) −0.976064 9.28663i −0.0546491 0.519952i
\(320\) −6.70820 0.967250i −0.375000 0.0540709i
\(321\) 33.0375 + 0.502571i 1.84398 + 0.0280508i
\(322\) 0.0258642 0.246082i 0.00144136 0.0137136i
\(323\) −4.56282 + 14.0429i −0.253882 + 0.781369i
\(324\) 6.46429 2.41869i 0.359127 0.134372i
\(325\) 3.36509 0.448416i 0.186662 0.0248736i
\(326\) 10.2602 + 17.7712i 0.568261 + 0.984256i
\(327\) 6.68585 + 21.6943i 0.369728 + 1.19970i
\(328\) 10.1800 4.53244i 0.562098 0.250262i
\(329\) 15.0050 6.68065i 0.827251 0.368316i
\(330\) 15.9222 + 24.5898i 0.876491 + 1.35363i
\(331\) −13.4822 6.00268i −0.741051 0.329937i 0.00125393 0.999999i \(-0.499601\pi\)
−0.742305 + 0.670062i \(0.766268\pi\)
\(332\) 13.9076 0.763278
\(333\) −2.40811 8.25811i −0.131963 0.452542i
\(334\) 3.44246 + 10.5948i 0.188363 + 0.579721i
\(335\) 30.5898 8.65322i 1.67130 0.472776i
\(336\) −11.5937 2.64926i −0.632491 0.144529i
\(337\) 11.9319 + 2.53619i 0.649970 + 0.138155i 0.521086 0.853504i \(-0.325527\pi\)
0.128884 + 0.991660i \(0.458861\pi\)
\(338\) −20.4015 4.33648i −1.10970 0.235873i
\(339\) 11.7573 + 2.68663i 0.638569 + 0.145918i
\(340\) 3.45213 + 1.27047i 0.187218 + 0.0689010i
\(341\) −9.08639 27.9650i −0.492056 1.51439i
\(342\) 23.7497 24.8153i 1.28424 1.34186i
\(343\) 16.7606 0.904989
\(344\) 2.29736 + 1.02285i 0.123865 + 0.0551485i
\(345\) −0.261583 + 0.322149i −0.0140832 + 0.0173439i
\(346\) −17.4744 + 7.78011i −0.939430 + 0.418261i
\(347\) 19.8592 8.84187i 1.06610 0.474656i 0.202730 0.979235i \(-0.435019\pi\)
0.863366 + 0.504578i \(0.168352\pi\)
\(348\) 0.803333 + 2.60666i 0.0430631 + 0.139732i
\(349\) 5.54554 + 9.60516i 0.296846 + 0.514152i 0.975413 0.220387i \(-0.0707319\pi\)
−0.678567 + 0.734539i \(0.737399\pi\)
\(350\) −10.1561 5.49361i −0.542866 0.293646i
\(351\) −3.41387 0.890174i −0.182219 0.0475140i
\(352\) 5.79531 17.8361i 0.308891 0.950669i
\(353\) −0.530083 + 5.04340i −0.0282135 + 0.268433i 0.971317 + 0.237789i \(0.0764226\pi\)
−0.999530 + 0.0306445i \(0.990244\pi\)
\(354\) 4.98923 + 0.0758967i 0.265174 + 0.00403387i
\(355\) −13.3768 + 27.1793i −0.709965 + 1.44253i
\(356\) −0.605357 5.75959i −0.0320838 0.305257i
\(357\) −4.67989 2.16951i −0.247686 0.114822i
\(358\) −7.46292 3.32271i −0.394427 0.175610i
\(359\) −9.46581 29.1328i −0.499586 1.53757i −0.809685 0.586864i \(-0.800362\pi\)
0.310099 0.950704i \(-0.399638\pi\)
\(360\) 9.56720 + 9.88913i 0.504236 + 0.521203i
\(361\) 8.76981 26.9907i 0.461569 1.42056i
\(362\) −2.32737 + 2.58480i −0.122324 + 0.135854i
\(363\) 15.4145 6.58388i 0.809049 0.345564i
\(364\) −0.483707 0.537211i −0.0253531 0.0281575i
\(365\) 13.1126 + 1.89069i 0.686342 + 0.0989632i
\(366\) 10.0022 4.27216i 0.522822 0.223310i
\(367\) −14.5972 6.49910i −0.761968 0.339250i −0.0113057 0.999936i \(-0.503599\pi\)
−0.750662 + 0.660686i \(0.770265\pi\)
\(368\) 0.529910 0.0276235
\(369\) −15.8317 3.87195i −0.824163 0.201565i
\(370\) −8.19434 + 6.82608i −0.426003 + 0.354871i
\(371\) 0.192986 1.83614i 0.0100193 0.0953276i
\(372\) 4.18096 + 7.50293i 0.216773 + 0.389009i
\(373\) 7.53730 + 8.37102i 0.390267 + 0.433435i 0.905976 0.423328i \(-0.139138\pi\)
−0.515710 + 0.856763i \(0.672472\pi\)
\(374\) 8.11274 14.0517i 0.419500 0.726595i
\(375\) 9.24425 + 17.0160i 0.477371 + 0.878702i
\(376\) 12.1334 + 21.0157i 0.625733 + 1.08380i
\(377\) 0.430852 1.32603i 0.0221900 0.0682938i
\(378\) 7.61419 + 9.27448i 0.391632 + 0.477028i
\(379\) −17.8996 13.0048i −0.919440 0.668012i 0.0239446 0.999713i \(-0.492377\pi\)
−0.943385 + 0.331701i \(0.892377\pi\)
\(380\) −11.0772 4.07668i −0.568247 0.209129i
\(381\) 12.4302 36.3646i 0.636819 1.86302i
\(382\) 8.54123 14.7938i 0.437007 0.756919i
\(383\) −0.661282 6.29168i −0.0337899 0.321490i −0.998340 0.0575909i \(-0.981658\pi\)
0.964550 0.263899i \(-0.0850086\pi\)
\(384\) 2.75413 22.8542i 0.140546 1.16627i
\(385\) −8.73065 + 11.0927i −0.444955 + 0.565338i
\(386\) 0.903967 2.78213i 0.0460107 0.141606i
\(387\) −1.74130 3.23978i −0.0885154 0.164687i
\(388\) 2.57638 + 7.92927i 0.130796 + 0.402548i
\(389\) −32.3577 + 6.87784i −1.64060 + 0.348720i −0.933551 0.358444i \(-0.883307\pi\)
−0.707049 + 0.707165i \(0.749974\pi\)
\(390\) 0.678501 + 4.32117i 0.0343572 + 0.218811i
\(391\) 0.224821 + 0.0477872i 0.0113697 + 0.00241670i
\(392\) 1.08758 + 10.3476i 0.0549309 + 0.522633i
\(393\) 1.79936 + 20.0489i 0.0907655 + 1.01133i
\(394\) 2.40786 + 1.07205i 0.121306 + 0.0540089i
\(395\) −20.0319 + 1.32880i −1.00791 + 0.0668591i
\(396\) −8.64675 + 5.88890i −0.434516 + 0.295928i
\(397\) 22.9141 + 16.6480i 1.15002 + 0.835541i 0.988484 0.151325i \(-0.0483539\pi\)
0.161540 + 0.986866i \(0.448354\pi\)
\(398\) −7.87134 + 1.67310i −0.394554 + 0.0838651i
\(399\) 15.0168 + 6.96149i 0.751779 + 0.348510i
\(400\) 9.42712 22.8608i 0.471356 1.14304i
\(401\) −4.98614 + 8.63625i −0.248996 + 0.431274i −0.963248 0.268615i \(-0.913434\pi\)
0.714251 + 0.699889i \(0.246767\pi\)
\(402\) 12.0634 + 39.1436i 0.601670 + 1.95231i
\(403\) 0.458929 4.36642i 0.0228609 0.217507i
\(404\) −7.57731 5.50524i −0.376985 0.273896i
\(405\) −2.21151 20.0027i −0.109891 0.993944i
\(406\) −3.83655 + 2.78742i −0.190405 + 0.138337i
\(407\) 6.51926 + 11.2917i 0.323148 + 0.559708i
\(408\) 2.46501 7.21139i 0.122036 0.357017i
\(409\) 9.44969 + 2.00859i 0.467257 + 0.0993186i 0.435523 0.900178i \(-0.356564\pi\)
0.0317346 + 0.999496i \(0.489897\pi\)
\(410\) 3.43772 + 19.9124i 0.169777 + 0.983402i
\(411\) −19.5181 + 21.0249i −0.962754 + 1.03708i
\(412\) −0.435711 + 0.483906i −0.0214659 + 0.0238403i
\(413\) 0.743021 + 2.28678i 0.0365617 + 0.112525i
\(414\) −0.422806 0.327290i −0.0207798 0.0160854i
\(415\) 9.95092 39.3116i 0.488471 1.92973i
\(416\) 1.87373 2.08099i 0.0918672 0.102029i
\(417\) −19.1739 21.9574i −0.938951 1.07526i
\(418\) −26.0321 + 45.0889i −1.27327 + 2.20537i
\(419\) 1.32174 + 12.5755i 0.0645710 + 0.614352i 0.978180 + 0.207758i \(0.0666168\pi\)
−0.913609 + 0.406594i \(0.866717\pi\)
\(420\) 1.87693 3.67158i 0.0915850 0.179155i
\(421\) 2.39672 22.8033i 0.116809 1.11136i −0.766393 0.642372i \(-0.777951\pi\)
0.883202 0.468992i \(-0.155383\pi\)
\(422\) −5.77800 4.19797i −0.281269 0.204354i
\(423\) 4.78191 35.1688i 0.232504 1.70996i
\(424\) 2.72771 0.132470
\(425\) 6.06116 8.84887i 0.294010 0.429233i
\(426\) −35.4111 16.4159i −1.71567 0.795352i
\(427\) 3.50695 + 3.89486i 0.169713 + 0.188485i
\(428\) 13.3647 5.95033i 0.646005 0.287620i
\(429\) 5.34696 + 0.0813386i 0.258154 + 0.00392706i
\(430\) −2.82035 + 3.58340i −0.136009 + 0.172807i
\(431\) 10.6124 7.71039i 0.511183 0.371397i −0.302089 0.953280i \(-0.597684\pi\)
0.813272 + 0.581883i \(0.197684\pi\)
\(432\) −18.0489 + 18.2933i −0.868376 + 0.880138i
\(433\) −19.0904 + 13.8700i −0.917425 + 0.666548i −0.942882 0.333128i \(-0.891896\pi\)
0.0254569 + 0.999676i \(0.491896\pi\)
\(434\) −9.99217 + 11.0974i −0.479639 + 0.532694i
\(435\) 7.94285 0.405647i 0.380831 0.0194493i
\(436\) 6.72557 + 7.46950i 0.322096 + 0.357724i
\(437\) −0.721404 0.153339i −0.0345094 0.00733521i
\(438\) −2.04228 + 16.9471i −0.0975840 + 0.809765i
\(439\) 7.92866 1.68529i 0.378414 0.0804344i −0.0147778 0.999891i \(-0.504704\pi\)
0.393192 + 0.919456i \(0.371371\pi\)
\(440\) −17.6473 11.1152i −0.841301 0.529896i
\(441\) 8.00617 12.9413i 0.381246 0.616254i
\(442\) 1.96001 1.42403i 0.0932280 0.0677341i
\(443\) −0.254259 0.440389i −0.0120802 0.0209235i 0.859922 0.510425i \(-0.170512\pi\)
−0.872002 + 0.489502i \(0.837179\pi\)
\(444\) −2.50514 2.86882i −0.118889 0.136148i
\(445\) −16.7133 2.40988i −0.792288 0.114239i
\(446\) −24.6295 + 10.9658i −1.16624 + 0.519244i
\(447\) −14.1842 + 23.7268i −0.670888 + 1.12224i
\(448\) 4.11609 0.874903i 0.194467 0.0413353i
\(449\) 7.22605 0.341018 0.170509 0.985356i \(-0.445459\pi\)
0.170509 + 0.985356i \(0.445459\pi\)
\(450\) −21.6413 + 12.4178i −1.02018 + 0.585380i
\(451\) 24.7040 1.16327
\(452\) 5.22317 1.11022i 0.245677 0.0522203i
\(453\) −7.09509 12.7325i −0.333356 0.598223i
\(454\) −13.9985 + 6.23256i −0.656984 + 0.292508i
\(455\) −1.86459 + 0.982883i −0.0874132 + 0.0460783i
\(456\) −7.90969 + 23.1398i −0.370405 + 1.08362i
\(457\) −7.94049 13.7533i −0.371441 0.643354i 0.618347 0.785905i \(-0.287803\pi\)
−0.989787 + 0.142551i \(0.954469\pi\)
\(458\) −11.0413 + 8.02199i −0.515927 + 0.374843i
\(459\) −9.30715 + 6.13354i −0.434421 + 0.286289i
\(460\) −0.0450869 + 0.178118i −0.00210219 + 0.00830478i
\(461\) −32.2855 + 6.86249i −1.50369 + 0.319618i −0.884840 0.465895i \(-0.845733\pi\)
−0.618845 + 0.785513i \(0.712399\pi\)
\(462\) −14.5504 10.9135i −0.676947 0.507740i
\(463\) −18.0119 3.82855i −0.837084 0.177928i −0.230625 0.973043i \(-0.574077\pi\)
−0.606459 + 0.795115i \(0.707411\pi\)
\(464\) −6.79566 7.54734i −0.315480 0.350377i
\(465\) 24.1995 6.44965i 1.12222 0.299096i
\(466\) −9.22069 + 10.2406i −0.427140 + 0.474387i
\(467\) −14.9196 + 10.8397i −0.690398 + 0.501603i −0.876791 0.480872i \(-0.840320\pi\)
0.186393 + 0.982475i \(0.440320\pi\)
\(468\) −1.53711 + 0.278147i −0.0710528 + 0.0128574i
\(469\) −15.9682 + 11.6016i −0.737344 + 0.535712i
\(470\) −42.3427 + 11.9779i −1.95312 + 0.552498i
\(471\) 0.0756744 0.126585i 0.00348689 0.00583275i
\(472\) −3.24531 + 1.44491i −0.149378 + 0.0665072i
\(473\) 3.73043 + 4.14306i 0.171525 + 0.190498i
\(474\) −2.31223 25.7634i −0.106204 1.18335i
\(475\) −19.4490 + 28.3942i −0.892381 + 1.30281i
\(476\) −2.28390 −0.104682
\(477\) −3.15477 2.44207i −0.144447 0.111815i
\(478\) 1.45226 + 1.05513i 0.0664250 + 0.0482606i
\(479\) 2.41271 22.9554i 0.110239 1.04886i −0.789894 0.613243i \(-0.789865\pi\)
0.900133 0.435614i \(-0.143469\pi\)
\(480\) 14.9046 + 5.74417i 0.680301 + 0.262184i
\(481\) 0.203500 + 1.93617i 0.00927881 + 0.0882820i
\(482\) −20.8726 + 36.1524i −0.950720 + 1.64670i
\(483\) 0.0833362 0.243800i 0.00379193 0.0110933i
\(484\) 4.96589 5.51518i 0.225722 0.250690i
\(485\) 24.2565 1.60904i 1.10143 0.0730627i
\(486\) 25.6994 3.44839i 1.16575 0.156422i
\(487\) −3.52725 10.8558i −0.159835 0.491921i 0.838784 0.544465i \(-0.183267\pi\)
−0.998619 + 0.0525435i \(0.983267\pi\)
\(488\) −5.18127 + 5.75439i −0.234545 + 0.260489i
\(489\) 6.29302 + 20.4197i 0.284580 + 0.923409i
\(490\) −18.6741 2.69260i −0.843608 0.121639i
\(491\) 38.9241 + 8.27356i 1.75662 + 0.373381i 0.969818 0.243828i \(-0.0784033\pi\)
0.786799 + 0.617209i \(0.211737\pi\)
\(492\) −7.08055 + 1.39280i −0.319216 + 0.0627924i
\(493\) −2.20253 3.81489i −0.0991969 0.171814i
\(494\) −6.28925 + 4.56941i −0.282967 + 0.205587i
\(495\) 10.4590 + 28.6547i 0.470095 + 1.28793i
\(496\) −25.8728 18.7977i −1.16172 0.844041i
\(497\) 1.96599 18.7051i 0.0881866 0.839039i
\(498\) 50.9360 + 11.6393i 2.28250 + 0.521568i
\(499\) 18.1188 31.3826i 0.811107 1.40488i −0.100983 0.994888i \(-0.532199\pi\)
0.912090 0.409990i \(-0.134468\pi\)
\(500\) 6.88208 + 5.11381i 0.307776 + 0.228697i
\(501\) 1.03690 + 11.5534i 0.0463253 + 0.516167i
\(502\) −37.7312 + 8.02001i −1.68403 + 0.357951i
\(503\) 26.1554 + 19.0030i 1.16621 + 0.847302i 0.990550 0.137149i \(-0.0437939\pi\)
0.175661 + 0.984451i \(0.443794\pi\)
\(504\) −7.69514 3.71055i −0.342769 0.165281i
\(505\) −20.9829 + 17.4792i −0.933725 + 0.777816i
\(506\) 0.740374 + 0.329636i 0.0329136 + 0.0146541i
\(507\) −19.7039 9.13434i −0.875081 0.405670i
\(508\) −1.77860 16.9223i −0.0789128 0.750805i
\(509\) 0.264168 + 0.0561506i 0.0117090 + 0.00248883i 0.213762 0.976886i \(-0.431428\pi\)
−0.202053 + 0.979374i \(0.564761\pi\)
\(510\) 11.5801 + 7.54215i 0.512774 + 0.333972i
\(511\) −8.04575 + 1.71018i −0.355923 + 0.0756538i
\(512\) −0.0335504 0.103257i −0.00148273 0.00456337i
\(513\) 29.8647 19.6812i 1.31856 0.868948i
\(514\) −10.7166 + 32.9823i −0.472689 + 1.45479i
\(515\) 1.05607 + 1.57783i 0.0465360 + 0.0695274i
\(516\) −1.30278 0.977145i −0.0573518 0.0430164i
\(517\) 5.62336 + 53.5027i 0.247315 + 2.35304i
\(518\) 3.31084 5.73454i 0.145470 0.251961i
\(519\) −19.5431 + 3.84429i −0.857847 + 0.168746i
\(520\) −1.73214 2.58792i −0.0759595 0.113488i
\(521\) 22.4017 + 16.2758i 0.981435 + 0.713054i 0.958029 0.286672i \(-0.0925489\pi\)
0.0234061 + 0.999726i \(0.492549\pi\)
\(522\) 0.760659 + 10.2191i 0.0332931 + 0.447279i
\(523\) 11.9194 36.6841i 0.521198 1.60408i −0.250515 0.968113i \(-0.580600\pi\)
0.771713 0.635971i \(-0.219400\pi\)
\(524\) 4.45627 + 7.71848i 0.194673 + 0.337183i
\(525\) −9.03523 7.93242i −0.394330 0.346199i
\(526\) −7.54477 + 13.0679i −0.328968 + 0.569789i
\(527\) −9.28170 10.3084i −0.404317 0.449040i
\(528\) 19.9869 33.4335i 0.869820 1.45500i
\(529\) 2.40295 22.8626i 0.104476 0.994025i
\(530\) −1.21377 + 4.79506i −0.0527229 + 0.208284i
\(531\) 5.04701 + 1.23435i 0.219021 + 0.0535660i
\(532\) 7.32855 0.317733
\(533\) 3.36976 + 1.50032i 0.145961 + 0.0649859i
\(534\) 2.60310 21.6009i 0.112647 0.934763i
\(535\) −7.25691 42.0344i −0.313744 1.81731i
\(536\) −19.5127 21.6711i −0.842820 0.936047i
\(537\) −6.80494 5.10401i −0.293655 0.220254i
\(538\) 16.5100 18.3362i 0.711798 0.790531i
\(539\) −7.12781 + 21.9371i −0.307016 + 0.944900i
\(540\) −4.61324 7.62320i −0.198522 0.328050i
\(541\) −9.26487 28.5143i −0.398328 1.22593i −0.926339 0.376690i \(-0.877062\pi\)
0.528011 0.849237i \(-0.322938\pi\)
\(542\) 11.9221 + 5.30808i 0.512099 + 0.228001i
\(543\) −2.96210 + 2.08400i −0.127116 + 0.0894331i
\(544\) −0.924776 8.79865i −0.0396494 0.377239i
\(545\) 25.9257 13.6662i 1.11053 0.585397i
\(546\) −1.32197 2.37233i −0.0565749 0.101526i
\(547\) −0.600529 + 5.71365i −0.0256768 + 0.244298i 0.974154 + 0.225886i \(0.0725277\pi\)
−0.999830 + 0.0184119i \(0.994139\pi\)
\(548\) −3.92511 + 12.0802i −0.167672 + 0.516042i
\(549\) 11.1443 2.01661i 0.475626 0.0860667i
\(550\) 27.3921 26.0762i 1.16800 1.11189i
\(551\) 7.06745 + 12.2412i 0.301083 + 0.521492i
\(552\) 0.371095 + 0.0847980i 0.0157949 + 0.00360924i
\(553\) 11.3870 5.06984i 0.484227 0.215592i
\(554\) 33.8065 15.0516i 1.43630 0.639483i
\(555\) −9.90152 + 5.02846i −0.420296 + 0.213446i
\(556\) −11.7910 5.24969i −0.500049 0.222636i
\(557\) −13.8510 −0.586887 −0.293444 0.955976i \(-0.594801\pi\)
−0.293444 + 0.955976i \(0.594801\pi\)
\(558\) 9.03342 + 30.9783i 0.382415 + 1.31141i
\(559\) 0.257236 + 0.791691i 0.0108799 + 0.0334850i
\(560\) −0.590686 + 15.3419i −0.0249610 + 0.648313i
\(561\) 11.4947 12.3822i 0.485309 0.522775i
\(562\) 16.5254 + 3.51258i 0.697081 + 0.148169i
\(563\) 29.1494 + 6.19591i 1.22850 + 0.261126i 0.776055 0.630665i \(-0.217218\pi\)
0.452447 + 0.891791i \(0.350551\pi\)
\(564\) −4.62820 15.0176i −0.194883 0.632357i
\(565\) 0.599018 15.5583i 0.0252009 0.654543i
\(566\) −0.392094 1.20674i −0.0164809 0.0507231i
\(567\) 5.57793 + 11.1808i 0.234251 + 0.469549i
\(568\) 27.7878 1.16595
\(569\) 14.9654 + 6.66301i 0.627381 + 0.279328i 0.695696 0.718336i \(-0.255096\pi\)
−0.0683159 + 0.997664i \(0.521763\pi\)
\(570\) −37.1580 24.2012i −1.55638 1.01368i
\(571\) −4.71944 + 2.10123i −0.197502 + 0.0879337i −0.503104 0.864226i \(-0.667809\pi\)
0.305602 + 0.952159i \(0.401142\pi\)
\(572\) 2.16300 0.963031i 0.0904397 0.0402663i
\(573\) 12.1019 13.0361i 0.505562 0.544592i
\(574\) −6.27303 10.8652i −0.261831 0.453505i
\(575\) 0.471213 + 0.254888i 0.0196509 + 0.0106295i
\(576\) 3.07166 8.55855i 0.127986 0.356606i
\(577\) 4.99821 15.3829i 0.208078 0.640399i −0.791495 0.611176i \(-0.790697\pi\)
0.999573 0.0292230i \(-0.00930328\pi\)
\(578\) −2.15574 + 20.5105i −0.0896668 + 0.853122i
\(579\) 1.56297 2.61448i 0.0649547 0.108654i
\(580\) 3.11508 1.64206i 0.129347 0.0681826i
\(581\) 2.63177 + 25.0396i 0.109184 + 1.03882i
\(582\) 2.79988 + 31.1969i 0.116059 + 1.29315i
\(583\) 5.52430 + 2.45958i 0.228793 + 0.101865i
\(584\) −3.75536 11.5578i −0.155398 0.478266i
\(585\) −0.313587 + 4.54385i −0.0129652 + 0.187865i
\(586\) 3.38744 10.4255i 0.139934 0.430672i
\(587\) −18.8057 + 20.8858i −0.776193 + 0.862050i −0.993474 0.114059i \(-0.963615\pi\)
0.217281 + 0.976109i \(0.430281\pi\)
\(588\) 0.806132 6.68939i 0.0332443 0.275866i
\(589\) 29.7830 + 33.0774i 1.22719 + 1.36293i
\(590\) −1.09592 6.34790i −0.0451182 0.261339i
\(591\) 2.19556 + 1.64677i 0.0903135 + 0.0677391i
\(592\) 12.9549 + 5.76791i 0.532444 + 0.237060i
\(593\) 3.80524 0.156262 0.0781312 0.996943i \(-0.475105\pi\)
0.0781312 + 0.996943i \(0.475105\pi\)
\(594\) −36.5969 + 14.3314i −1.50159 + 0.588025i
\(595\) −1.63414 + 6.45573i −0.0669931 + 0.264659i
\(596\) −1.27936 + 12.1723i −0.0524047 + 0.498597i
\(597\) −8.37836 0.127453i −0.342903 0.00521629i
\(598\) 0.0809718 + 0.0899283i 0.00331118 + 0.00367744i
\(599\) 17.5681 30.4289i 0.717813 1.24329i −0.244051 0.969762i \(-0.578476\pi\)
0.961864 0.273527i \(-0.0881902\pi\)
\(600\) 10.2601 14.5009i 0.418866 0.591995i
\(601\) −10.6092 18.3758i −0.432760 0.749563i 0.564350 0.825536i \(-0.309127\pi\)
−0.997110 + 0.0759732i \(0.975794\pi\)
\(602\) 0.874923 2.69274i 0.0356592 0.109748i
\(603\) 3.16596 + 42.5333i 0.128928 + 1.73209i
\(604\) −5.22110 3.79335i −0.212443 0.154349i
\(605\) −12.0363 17.9829i −0.489343 0.731107i
\(606\) −23.1443 26.5042i −0.940173 1.07666i
\(607\) −7.55362 + 13.0833i −0.306592 + 0.531033i −0.977615 0.210404i \(-0.932522\pi\)
0.671023 + 0.741437i \(0.265855\pi\)
\(608\) 2.96741 + 28.2330i 0.120344 + 1.14500i
\(609\) −4.54109 + 1.93961i −0.184014 + 0.0785969i
\(610\) −7.81012 11.6688i −0.316222 0.472454i
\(611\) −2.48225 + 7.63958i −0.100421 + 0.309064i
\(612\) −2.59647 + 4.19699i −0.104956 + 0.169653i
\(613\) −0.267857 0.824379i −0.0108186 0.0332963i 0.945501 0.325618i \(-0.105572\pi\)
−0.956320 + 0.292321i \(0.905572\pi\)
\(614\) 32.8776 6.98834i 1.32683 0.282026i
\(615\) −1.12922 + 21.0106i −0.0455345 + 0.847231i
\(616\) 12.6661 + 2.69226i 0.510331 + 0.108474i
\(617\) −2.07726 19.7638i −0.0836272 0.795660i −0.953299 0.302029i \(-0.902336\pi\)
0.869671 0.493631i \(-0.164331\pi\)
\(618\) −2.00076 + 1.40764i −0.0804823 + 0.0566237i
\(619\) 16.3619 + 7.28480i 0.657641 + 0.292801i 0.708296 0.705915i \(-0.249464\pi\)
−0.0506549 + 0.998716i \(0.516131\pi\)
\(620\) 8.51980 7.09720i 0.342163 0.285030i
\(621\) −0.353276 0.430309i −0.0141765 0.0172677i
\(622\) 24.0548 + 17.4768i 0.964510 + 0.700757i
\(623\) 10.2552 2.17980i 0.410864 0.0873319i
\(624\) 4.75680 3.34667i 0.190424 0.133974i
\(625\) 19.3790 15.7941i 0.775160 0.631765i
\(626\) 15.2615 26.4337i 0.609973 1.05650i
\(627\) −36.8842 + 39.7317i −1.47301 + 1.58673i
\(628\) 0.00682556 0.0649409i 0.000272370 0.00259142i
\(629\) 4.97615 + 3.61538i 0.198412 + 0.144155i
\(630\) 9.94695 11.8762i 0.396296 0.473160i
\(631\) −27.5034 + 19.9824i −1.09489 + 0.795487i −0.980219 0.197916i \(-0.936583\pi\)
−0.114675 + 0.993403i \(0.536583\pi\)
\(632\) 9.20786 + 15.9485i 0.366269 + 0.634396i
\(633\) −4.89154 5.60166i −0.194421 0.222646i
\(634\) 5.16248 + 1.09732i 0.205028 + 0.0435801i
\(635\) −49.1056 7.08050i −1.94870 0.280981i
\(636\) −1.72202 0.393495i −0.0682826 0.0156031i
\(637\) −2.30455 + 2.55946i −0.0913097 + 0.101410i
\(638\) −4.79979 14.7722i −0.190025 0.584838i
\(639\) −32.1383 24.8779i −1.27137 0.984154i
\(640\) −29.6529 + 1.96701i −1.17213 + 0.0777527i
\(641\) −8.52288 + 9.46562i −0.336634 + 0.373870i −0.887566 0.460680i \(-0.847606\pi\)
0.550932 + 0.834550i \(0.314272\pi\)
\(642\) 53.9274 10.6080i 2.12835 0.418664i
\(643\) 9.31365 16.1317i 0.367295 0.636173i −0.621847 0.783139i \(-0.713617\pi\)
0.989142 + 0.146966i \(0.0469507\pi\)
\(644\) −0.0119243 0.113453i −0.000469885 0.00447066i
\(645\) −3.69417 + 2.98333i −0.145458 + 0.117469i
\(646\) −2.56733 + 24.4265i −0.101010 + 0.961047i
\(647\) −2.58476 1.87794i −0.101617 0.0738294i 0.535816 0.844335i \(-0.320004\pi\)
−0.637434 + 0.770505i \(0.720004\pi\)
\(648\) −15.5670 + 9.92256i −0.611528 + 0.389795i
\(649\) −7.87544 −0.309138
\(650\) 5.32009 1.89338i 0.208671 0.0742643i
\(651\) −12.7173 + 8.94731i −0.498430 + 0.350673i
\(652\) 6.33041 + 7.03063i 0.247918 + 0.275341i
\(653\) −4.61992 + 2.05692i −0.180792 + 0.0804936i −0.495136 0.868815i \(-0.664882\pi\)
0.314345 + 0.949309i \(0.398215\pi\)
\(654\) 18.3809 + 32.9854i 0.718751 + 1.28983i
\(655\) 25.0057 7.07361i 0.977055 0.276389i
\(656\) 21.7371 15.7929i 0.848691 0.616610i
\(657\) −6.00419 + 16.7294i −0.234246 + 0.652678i
\(658\) 22.1034 16.0590i 0.861679 0.626046i
\(659\) 0.955484 1.06117i 0.0372204 0.0413374i −0.724247 0.689540i \(-0.757813\pi\)
0.761468 + 0.648203i \(0.224479\pi\)
\(660\) 9.53736 + 9.56283i 0.371241 + 0.372233i
\(661\) −3.11002 3.45402i −0.120966 0.134346i 0.679620 0.733564i \(-0.262145\pi\)
−0.800586 + 0.599219i \(0.795478\pi\)
\(662\) −24.0122 5.10395i −0.933261 0.198371i
\(663\) 2.31994 0.990900i 0.0900989 0.0384834i
\(664\) −36.3852 + 7.73391i −1.41202 + 0.300134i
\(665\) 5.24360 20.7151i 0.203338 0.803296i
\(666\) −6.77408 12.6035i −0.262490 0.488376i
\(667\) 0.178005 0.129328i 0.00689238 0.00500761i
\(668\) 2.56797 + 4.44786i 0.0993579 + 0.172093i
\(669\) −27.5453 + 5.41838i −1.06496 + 0.209487i
\(670\) 46.7784 24.6583i 1.80721 0.952635i
\(671\) −15.6821 + 6.98212i −0.605401 + 0.269542i
\(672\) −9.91628 0.150848i −0.382529 0.00581907i
\(673\) −18.4133 + 3.91386i −0.709780 + 0.150868i −0.548634 0.836062i \(-0.684852\pi\)
−0.161145 + 0.986931i \(0.551519\pi\)
\(674\) 20.2908 0.781572
\(675\) −24.8488 + 7.58549i −0.956429 + 0.291965i
\(676\) −9.61597 −0.369845
\(677\) 9.69731 2.06123i 0.372698 0.0792194i −0.0177547 0.999842i \(-0.505652\pi\)
0.390453 + 0.920623i \(0.372318\pi\)
\(678\) 20.0588 + 0.305137i 0.770354 + 0.0117187i
\(679\) −13.7885 + 6.13906i −0.529156 + 0.235595i
\(680\) −9.73802 1.40412i −0.373436 0.0538454i
\(681\) −15.6558 + 3.07962i −0.599930 + 0.118011i
\(682\) −24.4554 42.3580i −0.936445 1.62197i
\(683\) 21.4995 15.6203i 0.822655 0.597694i −0.0948166 0.995495i \(-0.530226\pi\)
0.917472 + 0.397801i \(0.130226\pi\)
\(684\) 8.33153 13.4673i 0.318564 0.514933i
\(685\) 31.3379 + 19.7383i 1.19736 + 0.754161i
\(686\) 27.2703 5.79649i 1.04119 0.221311i
\(687\) −13.0689 + 5.58205i −0.498611 + 0.212968i
\(688\) 5.93101 + 1.26068i 0.226118 + 0.0480628i
\(689\) 0.604171 + 0.671000i 0.0230171 + 0.0255631i
\(690\) −0.314196 + 0.614617i −0.0119612 + 0.0233981i
\(691\) −22.2009 + 24.6566i −0.844563 + 0.937982i −0.998746 0.0500602i \(-0.984059\pi\)
0.154183 + 0.988042i \(0.450725\pi\)
\(692\) −7.13452 + 5.18353i −0.271214 + 0.197048i
\(693\) −12.2388 14.4535i −0.464913 0.549042i
\(694\) 29.2539 21.2542i 1.11046 0.806799i
\(695\) −23.2754 + 29.5726i −0.882886 + 1.12175i
\(696\) −3.55124 6.37286i −0.134609 0.241563i
\(697\) 10.6465 4.74011i 0.403263 0.179544i
\(698\) 12.3447 + 13.7102i 0.467253 + 0.518938i
\(699\) −11.7354 + 8.25650i −0.443874 + 0.312290i
\(700\) −5.10659 1.50390i −0.193011 0.0568419i
\(701\) 26.1441 0.987451 0.493725 0.869618i \(-0.335635\pi\)
0.493725 + 0.869618i \(0.335635\pi\)
\(702\) −5.86239 0.267703i −0.221261 0.0101038i
\(703\) −15.9674 11.6010i −0.602223 0.437540i
\(704\) −1.44069 + 13.7073i −0.0542981 + 0.516612i
\(705\) −45.7608 + 2.33703i −1.72345 + 0.0880178i
\(706\) 0.881738 + 8.38918i 0.0331846 + 0.315731i
\(707\) 8.47791 14.6842i 0.318845 0.552255i
\(708\) 2.25722 0.444015i 0.0848316 0.0166871i
\(709\) 26.7119 29.6666i 1.00319 1.11415i 0.00973033 0.999953i \(-0.496903\pi\)
0.993458 0.114201i \(-0.0364306\pi\)
\(710\) −12.3649 + 48.8483i −0.464048 + 1.83324i
\(711\) 3.62892 26.6890i 0.136095 1.00092i
\(712\) 4.78661 + 14.7317i 0.179386 + 0.552093i
\(713\) 0.463608 0.514888i 0.0173622 0.0192827i
\(714\) −8.36470 1.91140i −0.313041 0.0715322i
\(715\) −1.17449 6.80306i −0.0439236 0.254420i
\(716\) −3.68398 0.783055i −0.137677 0.0292641i
\(717\) 1.22946 + 1.40794i 0.0459149 + 0.0525805i
\(718\) −25.4766 44.1267i −0.950777 1.64679i
\(719\) 32.4317 23.5630i 1.20950 0.878751i 0.214312 0.976765i \(-0.431249\pi\)
0.995185 + 0.0980142i \(0.0312491\pi\)
\(720\) 27.5214 + 18.5270i 1.02566 + 0.690462i
\(721\) −0.953688 0.692895i −0.0355172 0.0258048i
\(722\) 4.93444 46.9481i 0.183641 1.74723i
\(723\) −29.5739 + 31.8570i −1.09986 + 1.18477i
\(724\) −0.801787 + 1.38874i −0.0297982 + 0.0516120i
\(725\) −2.41263 9.98006i −0.0896029 0.370650i
\(726\) 22.8031 16.0432i 0.846301 0.595419i
\(727\) 34.5304 7.33967i 1.28066 0.272213i 0.483162 0.875531i \(-0.339488\pi\)
0.797501 + 0.603318i \(0.206155\pi\)
\(728\) 1.56422 + 1.13647i 0.0579738 + 0.0421204i
\(729\) 26.8876 + 2.46075i 0.995838 + 0.0911390i
\(730\) 21.9886 1.45860i 0.813835 0.0539852i
\(731\) 2.40262 + 1.06972i 0.0888641 + 0.0395649i
\(732\) 4.10108 2.88534i 0.151580 0.106645i
\(733\) −0.702668 6.68544i −0.0259536 0.246932i −0.999805 0.0197463i \(-0.993714\pi\)
0.973851 0.227186i \(-0.0729525\pi\)
\(734\) −25.9980 5.52604i −0.959603 0.203970i
\(735\) −18.3316 7.06491i −0.676172 0.260593i
\(736\) 0.432244 0.0918764i 0.0159327 0.00338661i
\(737\) −19.9773 61.4839i −0.735874 2.26479i
\(738\) −27.0979 0.824624i −0.997488 0.0303548i
\(739\) −3.30815 + 10.1814i −0.121692 + 0.374530i −0.993284 0.115702i \(-0.963088\pi\)
0.871592 + 0.490233i \(0.163088\pi\)
\(740\) −3.04102 + 3.86376i −0.111790 + 0.142035i
\(741\) −7.44419 + 3.17959i −0.273469 + 0.116805i
\(742\) −0.321012 3.05423i −0.0117847 0.112124i
\(743\) −10.6028 + 18.3647i −0.388981 + 0.673735i −0.992313 0.123756i \(-0.960506\pi\)
0.603332 + 0.797490i \(0.293839\pi\)
\(744\) −15.1106 17.3043i −0.553982 0.634405i
\(745\) 33.4912 + 12.3256i 1.22702 + 0.451575i
\(746\) 15.1586 + 11.0133i 0.554995 + 0.403227i
\(747\) 49.0058 + 23.6303i 1.79303 + 0.864586i
\(748\) 2.31161 7.11441i 0.0845209 0.260129i
\(749\) 13.2422 + 22.9361i 0.483858 + 0.838067i
\(750\) 20.9256 + 24.4888i 0.764096 + 0.894204i
\(751\) −24.6961 + 42.7750i −0.901175 + 1.56088i −0.0752042 + 0.997168i \(0.523961\pi\)
−0.825971 + 0.563713i \(0.809372\pi\)
\(752\) 39.1515 + 43.4822i 1.42771 + 1.58563i
\(753\) −40.1616 0.610943i −1.46357 0.0222640i
\(754\) 0.242424 2.30651i 0.00882857 0.0839982i
\(755\) −14.4581 + 12.0439i −0.526184 + 0.438324i
\(756\) 4.32271 + 3.45257i 0.157215 + 0.125569i
\(757\) −31.2549 −1.13598 −0.567989 0.823036i \(-0.692279\pi\)
−0.567989 + 0.823036i \(0.692279\pi\)
\(758\) −33.6210 14.9690i −1.22117 0.543700i
\(759\) 0.675098 + 0.506353i 0.0245045 + 0.0183795i
\(760\) 31.2473 + 4.50552i 1.13346 + 0.163432i
\(761\) −19.3977 21.5434i −0.703168 0.780947i 0.280709 0.959793i \(-0.409430\pi\)
−0.983877 + 0.178846i \(0.942764\pi\)
\(762\) 7.64820 63.4658i 0.277065 2.29912i
\(763\) −12.1756 + 13.5224i −0.440786 + 0.489543i
\(764\) 2.43370 7.49016i 0.0880482 0.270985i
\(765\) 10.0055 + 10.3422i 0.361751 + 0.373924i
\(766\) −3.25185 10.0082i −0.117494 0.361610i
\(767\) −1.07425 0.478289i −0.0387891 0.0172700i
\(768\) −2.48420 27.6796i −0.0896409 0.998800i
\(769\) −3.56272 33.8970i −0.128475 1.22236i −0.848797 0.528719i \(-0.822673\pi\)
0.720322 0.693640i \(-0.243994\pi\)
\(770\) −10.3689 + 21.0678i −0.373668 + 0.759230i
\(771\) −18.5291 + 30.9948i −0.667309 + 1.11625i
\(772\) 0.140974 1.34128i 0.00507377 0.0482737i
\(773\) −9.44334 + 29.0636i −0.339653 + 1.04535i 0.624731 + 0.780840i \(0.285209\pi\)
−0.964384 + 0.264506i \(0.914791\pi\)
\(774\) −3.95362 4.66906i −0.142110 0.167826i
\(775\) −13.9652 29.1604i −0.501645 1.04747i
\(776\) −11.1498 19.3120i −0.400253 0.693259i
\(777\) 4.69105 5.05320i 0.168290 0.181283i
\(778\) −50.2688 + 22.3811i −1.80223 + 0.802402i
\(779\) −34.1622 + 15.2100i −1.22399 + 0.544955i
\(780\) 0.720183 + 1.88364i 0.0257867 + 0.0674453i
\(781\) 56.2771 + 25.0562i 2.01375 + 0.896581i
\(782\) 0.382321 0.0136718
\(783\) −1.59828 + 10.5500i −0.0571177 + 0.377025i
\(784\) 7.75234 + 23.8592i 0.276869 + 0.852116i
\(785\) −0.178680 0.0657588i −0.00637736 0.00234703i
\(786\) 9.86132 + 31.9981i 0.351742 + 1.14134i
\(787\) 22.4498 + 4.77185i 0.800249 + 0.170098i 0.589845 0.807517i \(-0.299189\pi\)
0.210404 + 0.977615i \(0.432522\pi\)
\(788\) 1.18861 + 0.252647i 0.0423425 + 0.00900017i
\(789\) −10.6900 + 11.5153i −0.380574 + 0.409955i
\(790\) −32.1332 + 9.08982i −1.14325 + 0.323401i
\(791\) 2.98726 + 9.19384i 0.106215 + 0.326895i
\(792\) 19.3470 20.2150i 0.687465 0.718310i
\(793\) −2.56316 −0.0910205
\(794\) 43.0398 + 19.1626i 1.52743 + 0.680054i
\(795\) −2.34437 + 4.58597i −0.0831464 + 0.162647i
\(796\) −3.38929 + 1.50901i −0.120130 + 0.0534854i
\(797\) 39.7228 17.6857i 1.40705 0.626461i 0.444063 0.895996i \(-0.353537\pi\)
0.962991 + 0.269535i \(0.0868699\pi\)
\(798\) 26.8406 + 6.13327i 0.950145 + 0.217115i
\(799\) 12.6893 + 21.9786i 0.448916 + 0.777545i
\(800\) 3.72601 20.2819i 0.131734 0.717075i
\(801\) 7.65298 21.3235i 0.270405 0.753427i
\(802\) −5.12593 + 15.7760i −0.181003 + 0.557070i
\(803\) 2.81613 26.7937i 0.0993790 0.945528i
\(804\) 9.19225 + 16.4959i 0.324186 + 0.581766i
\(805\) −0.329220 0.0474700i −0.0116035 0.00167310i
\(806\) −0.763381 7.26308i −0.0268889 0.255831i
\(807\) 21.0127 14.7836i 0.739684 0.520408i
\(808\) 22.8853 + 10.1892i 0.805102 + 0.358455i
\(809\) −8.36599 25.7479i −0.294133 0.905247i −0.983511 0.180846i \(-0.942116\pi\)
0.689379 0.724401i \(-0.257884\pi\)
\(810\) −10.5160 31.7805i −0.369493 1.11665i
\(811\) −11.3390 + 34.8979i −0.398167 + 1.22543i 0.528300 + 0.849058i \(0.322829\pi\)
−0.926468 + 0.376375i \(0.877171\pi\)
\(812\) −1.46295 + 1.62477i −0.0513395 + 0.0570182i
\(813\) 10.8710 + 8.15373i 0.381263 + 0.285964i
\(814\) 14.5122 + 16.1175i 0.508654 + 0.564918i
\(815\) 24.4024 12.8633i 0.854779 0.450581i
\(816\) 2.19851 18.2435i 0.0769632 0.638651i
\(817\) −7.70951 3.43249i −0.269721 0.120088i
\(818\) 16.0697 0.561865
\(819\) −0.791654 2.71482i −0.0276626 0.0948634i
\(820\) 3.45897 + 8.65018i 0.120793 + 0.302078i
\(821\) −0.158330 + 1.50641i −0.00552576 + 0.0525741i −0.996937 0.0782049i \(-0.975081\pi\)
0.991412 + 0.130779i \(0.0417478\pi\)
\(822\) −24.4855 + 40.9586i −0.854031 + 1.42859i
\(823\) −24.3576 27.0519i −0.849053 0.942969i 0.149900 0.988701i \(-0.452105\pi\)
−0.998954 + 0.0457319i \(0.985438\pi\)
\(824\) 0.870816 1.50830i 0.0303363 0.0525440i
\(825\) 33.8546 20.1163i 1.17867 0.700361i
\(826\) 1.99979 + 3.46374i 0.0695816 + 0.120519i
\(827\) −0.131104 + 0.403496i −0.00455892 + 0.0140309i −0.953310 0.301993i \(-0.902348\pi\)
0.948751 + 0.316024i \(0.102348\pi\)
\(828\) −0.222042 0.107067i −0.00771648 0.00372083i
\(829\) −15.0808 10.9568i −0.523778 0.380547i 0.294247 0.955729i \(-0.404931\pi\)
−0.818025 + 0.575182i \(0.804931\pi\)
\(830\) 2.59512 67.4032i 0.0900780 2.33960i
\(831\) 37.8087 7.43728i 1.31157 0.257997i
\(832\) −1.02898 + 1.78225i −0.0356736 + 0.0617885i
\(833\) 1.13741 + 10.8217i 0.0394088 + 0.374950i
\(834\) −38.7906 29.0947i −1.34321 1.00747i
\(835\) 14.4098 4.07625i 0.498673 0.141064i
\(836\) −7.41748 + 22.8286i −0.256539 + 0.789545i
\(837\) 1.98419 + 33.5417i 0.0685835 + 1.15937i
\(838\) 6.49962 + 20.0038i 0.224526 + 0.691019i
\(839\) 28.4120 6.03916i 0.980892 0.208495i 0.310558 0.950554i \(-0.399484\pi\)
0.670334 + 0.742059i \(0.266151\pi\)
\(840\) −2.86872 + 10.6494i −0.0989803 + 0.367439i
\(841\) 24.2415 + 5.15270i 0.835915 + 0.177679i
\(842\) −3.98670 37.9309i −0.137391 1.30718i
\(843\) 15.9603 + 7.39888i 0.549702 + 0.254831i
\(844\) −3.00805 1.33927i −0.103541 0.0460996i
\(845\) −6.88026 + 27.1808i −0.236688 + 0.935047i
\(846\) −4.38235 58.8750i −0.150668 2.02416i
\(847\) 10.8694 + 7.89708i 0.373477 + 0.271347i
\(848\) 6.43322 1.36742i 0.220918 0.0469575i
\(849\) −0.118102 1.31592i −0.00405326 0.0451624i
\(850\) 6.80151 16.4937i 0.233290 0.565730i
\(851\) −0.153613 + 0.266066i −0.00526580 + 0.00912063i
\(852\) −17.5426 4.00861i −0.600998 0.137333i
\(853\) −1.83844 + 17.4915i −0.0629468 + 0.598899i 0.916896 + 0.399127i \(0.130687\pi\)
−0.979842 + 0.199772i \(0.935980\pi\)
\(854\) 7.05296 + 5.12428i 0.241347 + 0.175349i
\(855\) −32.1057 33.1860i −1.09799 1.13494i
\(856\) −31.6559 + 22.9993i −1.08198 + 0.786101i
\(857\) −4.22020 7.30960i −0.144159 0.249691i 0.784900 0.619623i \(-0.212714\pi\)
−0.929059 + 0.369932i \(0.879381\pi\)
\(858\) 8.72788 1.71685i 0.297965 0.0586122i
\(859\) 33.0228 + 7.01920i 1.12672 + 0.239492i 0.733326 0.679877i \(-0.237967\pi\)
0.393396 + 0.919369i \(0.371300\pi\)
\(860\) −0.928383 + 1.88632i −0.0316576 + 0.0643229i
\(861\) −3.84751 12.4845i −0.131123 0.425469i
\(862\) 14.6004 16.2154i 0.497291 0.552298i
\(863\) 12.9265 + 39.7837i 0.440023 + 1.35425i 0.887851 + 0.460132i \(0.152198\pi\)
−0.447828 + 0.894120i \(0.647802\pi\)
\(864\) −11.5506 + 18.0511i −0.392960 + 0.614111i
\(865\) 9.54714 + 23.8755i 0.324613 + 0.811790i
\(866\) −26.2641 + 29.1693i −0.892492 + 0.991213i
\(867\) −6.94591 + 20.3203i −0.235896 + 0.690114i
\(868\) −3.44234 + 5.96231i −0.116841 + 0.202374i
\(869\) 4.26748 + 40.6024i 0.144764 + 1.37734i
\(870\) 12.7831 3.40696i 0.433388 0.115507i
\(871\) 1.00900 9.60000i 0.0341887 0.325283i
\(872\) −21.7493 15.8018i −0.736523 0.535115i
\(873\) −4.39425 + 32.3177i −0.148723 + 1.09379i
\(874\) −1.22679 −0.0414967
\(875\) −7.90474 + 13.3584i −0.267229 + 0.451596i
\(876\) 0.703473 + 7.83826i 0.0237681 + 0.264830i
\(877\) −19.1882 21.3106i −0.647938 0.719608i 0.326266 0.945278i \(-0.394210\pi\)
−0.974204 + 0.225670i \(0.927543\pi\)
\(878\) 12.3175 5.48408i 0.415694 0.185079i
\(879\) 5.85692 9.79724i 0.197549 0.330453i
\(880\) −47.1926 17.3681i −1.59086 0.585477i
\(881\) −11.7352 + 8.52611i −0.395368 + 0.287252i −0.767652 0.640867i \(-0.778575\pi\)
0.372283 + 0.928119i \(0.378575\pi\)
\(882\) 8.55078 23.8250i 0.287920 0.802229i
\(883\) −42.8896 + 31.1611i −1.44335 + 1.04865i −0.456019 + 0.889970i \(0.650725\pi\)
−0.987329 + 0.158684i \(0.949275\pi\)
\(884\) 0.747387 0.830057i 0.0251373 0.0279178i
\(885\) 0.359986 6.69802i 0.0121008 0.225152i
\(886\) −0.565995 0.628601i −0.0190150 0.0211183i
\(887\) 8.79953 + 1.87040i 0.295459 + 0.0628018i 0.353256 0.935527i \(-0.385074\pi\)
−0.0577971 + 0.998328i \(0.518408\pi\)
\(888\) 8.14932 + 6.11235i 0.273473 + 0.205117i
\(889\) 30.1308 6.40449i 1.01055 0.214800i
\(890\) −28.0268 + 1.85914i −0.939461 + 0.0623185i
\(891\) −40.4741 + 6.05894i −1.35593 + 0.202982i
\(892\) −10.0558 + 7.30599i −0.336694 + 0.244623i
\(893\) −40.7174 70.5246i −1.36256 2.36001i
\(894\) −14.8726 + 43.5100i −0.497415 + 1.45519i
\(895\) −4.84931 + 9.85297i −0.162094 + 0.329349i
\(896\) 16.8561 7.50483i 0.563123 0.250719i
\(897\) 0.0613354 + 0.110069i 0.00204793 + 0.00367510i
\(898\) 11.7571 2.49905i 0.392340 0.0833944i
\(899\) −13.2788 −0.442872
\(900\) −8.56910 + 7.67437i −0.285637 + 0.255812i
\(901\) 2.85269 0.0950369
\(902\) 40.1946 8.54362i 1.33833 0.284471i
\(903\) 1.51275 2.53047i 0.0503411 0.0842089i
\(904\) −13.0475 + 5.80914i −0.433955 + 0.193209i
\(905\) 3.35176 + 3.26000i 0.111416 + 0.108366i
\(906\) −15.9474 18.2625i −0.529818 0.606733i
\(907\) 13.0147 + 22.5421i 0.432145 + 0.748498i 0.997058 0.0766530i \(-0.0244234\pi\)
−0.564912 + 0.825151i \(0.691090\pi\)
\(908\) −5.71538 + 4.15247i −0.189672 + 0.137804i
\(909\) −17.3461 32.2732i −0.575333 1.07044i
\(910\) −2.69385 + 2.24404i −0.0893003 + 0.0743893i
\(911\) −3.92226 + 0.833703i −0.129950 + 0.0276218i −0.272428 0.962176i \(-0.587827\pi\)
0.142477 + 0.989798i \(0.454493\pi\)
\(912\) −7.05455 + 58.5396i −0.233600 + 1.93844i
\(913\) −80.6628 17.1454i −2.66955 0.567430i
\(914\) −17.6760 19.6312i −0.584670 0.649342i
\(915\) −5.22143 13.6567i −0.172615 0.451477i
\(916\) −4.21026 + 4.67597i −0.139111 + 0.154498i
\(917\) −13.0533 + 9.48377i −0.431058 + 0.313182i
\(918\) −13.0220 + 13.1983i −0.429788 + 0.435610i
\(919\) 0.331871 0.241118i 0.0109474 0.00795375i −0.582298 0.812975i \(-0.697846\pi\)
0.593245 + 0.805022i \(0.297846\pi\)
\(920\) 0.0189068 0.491067i 0.000623339 0.0161900i
\(921\) 34.9953 + 0.532353i 1.15314 + 0.0175416i
\(922\) −50.1567 + 22.3312i −1.65182 + 0.735439i
\(923\) 6.15481 + 6.83561i 0.202588 + 0.224997i
\(924\) −7.60779 3.52682i −0.250278 0.116024i
\(925\) 8.74557 + 11.3604i 0.287552 + 0.373526i
\(926\) −30.6303 −1.00657
\(927\) −2.35750 + 0.964814i −0.0774306 + 0.0316887i
\(928\) −6.85175 4.97808i −0.224920 0.163414i
\(929\) 0.704207 6.70008i 0.0231043 0.219822i −0.976878 0.213799i \(-0.931416\pi\)
0.999982 0.00602306i \(-0.00191721\pi\)
\(930\) 37.1431 18.8630i 1.21797 0.618543i
\(931\) −3.64970 34.7246i −0.119614 1.13805i
\(932\) −3.17656 + 5.50196i −0.104052 + 0.180223i
\(933\) 20.3643 + 23.3206i 0.666698 + 0.763484i
\(934\) −20.5261 + 22.7966i −0.671635 + 0.745926i
\(935\) −18.4558 11.6244i −0.603570 0.380160i
\(936\) 3.86673 1.58247i 0.126388 0.0517246i
\(937\) −13.0786 40.2519i −0.427260 1.31497i −0.900814 0.434206i \(-0.857029\pi\)
0.473554 0.880765i \(-0.342971\pi\)
\(938\) −21.9688 + 24.3988i −0.717305 + 0.796648i
\(939\) 21.6237 23.2931i 0.705662 0.760141i
\(940\) −17.9468 + 9.46030i −0.585359 + 0.308561i
\(941\) −51.2834 10.9006i −1.67179 0.355350i −0.727919 0.685663i \(-0.759512\pi\)
−0.943871 + 0.330314i \(0.892846\pi\)
\(942\) 0.0793475 0.232131i 0.00258528 0.00756325i
\(943\) 0.291050 + 0.504114i 0.00947790 + 0.0164162i
\(944\) −6.92961 + 5.03466i −0.225540 + 0.163864i
\(945\) 12.8521 9.74836i 0.418077 0.317114i
\(946\) 7.50241 + 5.45082i 0.243924 + 0.177221i
\(947\) −0.245164 + 2.33258i −0.00796675 + 0.0757985i −0.997783 0.0665533i \(-0.978800\pi\)
0.989816 + 0.142352i \(0.0454664\pi\)
\(948\) −3.51227 11.3967i −0.114073 0.370146i
\(949\) 2.01136 3.48378i 0.0652915 0.113088i
\(950\) −21.8246 + 52.9249i −0.708084 + 1.71711i
\(951\) 4.98595 + 2.31139i 0.161681 + 0.0749519i
\(952\) 5.97517 1.27006i 0.193656 0.0411629i
\(953\) −7.72986 5.61607i −0.250395 0.181922i 0.455507 0.890232i \(-0.349458\pi\)
−0.705902 + 0.708310i \(0.749458\pi\)
\(954\) −5.97752 2.88232i −0.193530 0.0933186i
\(955\) −19.4306 12.2384i −0.628759 0.396026i
\(956\) 0.756054 + 0.336617i 0.0244525 + 0.0108870i
\(957\) −1.44574 16.1088i −0.0467341 0.520723i
\(958\) −4.01328 38.1839i −0.129663 1.23366i
\(959\) −22.4924 4.78090i −0.726316 0.154383i
\(960\) −11.5921 1.85186i −0.374134 0.0597686i
\(961\) −10.5779 + 2.24839i −0.341221 + 0.0725288i
\(962\) 1.00071 + 3.07987i 0.0322642 + 0.0992989i
\(963\) 57.2028 + 1.74076i 1.84334 + 0.0560951i
\(964\) −5.94735 + 18.3041i −0.191551 + 0.589534i
\(965\) −3.69043 1.35817i −0.118799 0.0437211i
\(966\) 0.0512760 0.425495i 0.00164978 0.0136901i
\(967\) −2.15909 20.5424i −0.0694318 0.660599i −0.972786 0.231705i \(-0.925570\pi\)
0.903354 0.428895i \(-0.141097\pi\)
\(968\) −9.92488 + 17.1904i −0.318998 + 0.552520i
\(969\) −8.27208 + 24.2000i −0.265738 + 0.777417i
\(970\) 38.9100 11.0068i 1.24932 0.353408i
\(971\) 24.5224 + 17.8166i 0.786962 + 0.571761i 0.907060 0.421001i \(-0.138321\pi\)
−0.120098 + 0.992762i \(0.538321\pi\)
\(972\) 11.2589 4.01850i 0.361130 0.128894i
\(973\) 7.22044 22.2222i 0.231477 0.712412i
\(974\) −9.49335 16.4430i −0.304186 0.526866i
\(975\) 5.83965 0.687935i 0.187019 0.0220316i
\(976\) −9.33514 + 16.1689i −0.298810 + 0.517555i
\(977\) −15.7527 17.4951i −0.503973 0.559719i 0.436448 0.899729i \(-0.356236\pi\)
−0.940422 + 0.340010i \(0.889570\pi\)
\(978\) 17.3010 + 31.0474i 0.553224 + 0.992786i
\(979\) −3.58946 + 34.1514i −0.114719 + 1.09148i
\(980\) −8.67937 + 0.575740i −0.277252 + 0.0183913i
\(981\) 11.0073 + 37.7474i 0.351437 + 1.20518i
\(982\) 66.1926 2.11229
\(983\) 17.6593 + 7.86243i 0.563245 + 0.250773i 0.668550 0.743667i \(-0.266915\pi\)
−0.105305 + 0.994440i \(0.533582\pi\)
\(984\) 17.7497 7.58132i 0.565840 0.241684i
\(985\) 1.56459 3.17899i 0.0498521 0.101291i
\(986\) −4.90295 5.44528i −0.156142 0.173413i
\(987\) 26.1624 11.1746i 0.832758 0.355691i
\(988\) −2.39821 + 2.66348i −0.0762971 + 0.0847365i
\(989\) −0.0405939 + 0.124935i −0.00129081 + 0.00397271i
\(990\) 26.9271 + 43.0054i 0.855800 + 1.36680i
\(991\) −0.458610 1.41146i −0.0145682 0.0448364i 0.943508 0.331349i \(-0.107504\pi\)
−0.958076 + 0.286513i \(0.907504\pi\)
\(992\) −24.3635 10.8473i −0.773540 0.344402i
\(993\) −23.1911 10.7509i −0.735947 0.341171i
\(994\) −3.27021 31.1140i −0.103725 0.986876i
\(995\) 1.84036 + 10.6600i 0.0583433 + 0.337944i
\(996\) 24.0859 + 0.366397i 0.763189 + 0.0116097i
\(997\) 1.65392 15.7360i 0.0523803 0.498365i −0.936609 0.350377i \(-0.886053\pi\)
0.988989 0.147988i \(-0.0472798\pi\)
\(998\) 18.6267 57.3271i 0.589619 1.81466i
\(999\) −3.95292 14.3653i −0.125065 0.454496i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 225.2.q.a.121.22 yes 224
3.2 odd 2 675.2.r.a.496.7 224
9.2 odd 6 675.2.r.a.46.22 224
9.7 even 3 inner 225.2.q.a.196.7 yes 224
25.6 even 5 inner 225.2.q.a.31.7 224
75.56 odd 10 675.2.r.a.631.22 224
225.56 odd 30 675.2.r.a.181.7 224
225.106 even 15 inner 225.2.q.a.106.22 yes 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.q.a.31.7 224 25.6 even 5 inner
225.2.q.a.106.22 yes 224 225.106 even 15 inner
225.2.q.a.121.22 yes 224 1.1 even 1 trivial
225.2.q.a.196.7 yes 224 9.7 even 3 inner
675.2.r.a.46.22 224 9.2 odd 6
675.2.r.a.181.7 224 225.56 odd 30
675.2.r.a.496.7 224 3.2 odd 2
675.2.r.a.631.22 224 75.56 odd 10